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Preprint 2006-016

Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source

Cleopatra Christoforou

Abstract: Global weak solutions of a strictly hyperbolic system of balance laws in one-space dimension were constructed (cf. Christoforou [C]) via the vanishing viscosity method under the assumption that the source term g is dissipative. In this article, we establish sharp estimates on the uniformly Lipschitz semigroup P generated by the vanishing viscosity limit in the general case which includes also non-conservative systems. Furthermore, we prove uniqueness of solutions by means of local integral estimates and show that every viscosity solution can be constructed as a limit of vanishing viscosity approximations.

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Cleopatra Christoforou,
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; 2006-05-03.